26 REPORT OF THE SECRETARY. 



analytic form, wliicli applies very correctly at higher altitudes and 

 near the zenith. For low altitudes, Laplace combined the same assump- 

 tion with his theory of refraction, and derived an approximate expres- 

 sion for the relative amounts. 



But the inquiry arises how far the fundamental assumption is sus- 

 tained by experiments. During the trigonometric survey of India, 

 the astronomer, Jacob, observed the extinction of light reflected 

 through an extent of sixty miles of horizontal atmosphere. His results 

 were found to correspond very nearly with the law that "as the 

 first differences of distance increases in arithmetical progression, the 

 intensity of light diminishes in geometrical progression." The ex- 

 periments of Delaroche and Melloni also indicate that the hypothesis 

 of equal thicknesses absorbing equal portions of the incident heat, is 

 only an approximation, which, in extended media, will differ widely 

 from the truth ; indeed, their experiments show an increasing facility 

 of transmission through equal strata in the direction in which the 

 rays proceed. 



The necessity of a change, therefore, in the theory of atmospheric ab- 

 sorption to render it conformable to such experiments being obvious, the 

 greater part of Mr. Meech's time available during the past year has 

 been devoted to this object. The remaining discussions relative to 

 the theory of climatic heat^ of which this forms a part, are yet in 

 progress. It may here be stated, however, that on computing by this 

 method the observations given in the translation of Kaemtz's Meteor- 

 ology, p. 150, Mr. Meech shows that out of 100 rays descending 

 vertically from the zenith, 22 rays are lost or absorbed in the atmo- 

 sphere, and 78 are transmitted to the earth's surface. The same pro- 

 cess applied to the mean of observations made with Herschel's actino- 

 meter on the Faulhorn and at Brientz, in Switzerland, leads to 

 precisely the same result when reduced to the sea level. 



6. A proposition was made to the Institution in 1856 by Dr. James 

 Deane, of Greenfield, Massachusetts, to publish a memoir containing 

 a series of illustrations of his researches relative to the celebrated fossil 

 foot-prints in the sandstone of the Connecticut valley. It is now well 

 established that these foot-prints consist of impressions made by gigantic 

 birds and other animals, and were first brought to the attention of the 

 scientific world by the ardent and persevering efforts of Dr. Deane 

 and the critical investigations of Professor Hitchcock. The number 

 of plates required to illustrate the memoir, as originally proposed, 

 would have involved too great an expense to be met in one or even 



